List of top Mathematics Questions asked in MET

The length of the axis of the conic \(9x^2 + 4y^2 - 6x + 4y + 1 = 0\) are

The equation of the parabola whose vertex is (-1, -2), axis is vertical and which passes through the point (3, 6), is

If \(f(x) = \cot^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right)\) and \(g(x) = \cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right)\), then \(\lim_{x \to a} \frac{f(x) - f(a)}{g(x) - g(a)}\), \(0<a<1/2\), is

\(\lim_{x \to -2} \frac{\sin^{-1}(x + 2)}{x^2 + 2x}\) is equal to

If \(c = 2\cos\theta\), then the value of the determinant \(\Delta = \begin{vmatrix} c & 1 & 0 \\ 1 & c & 1 \\ 6 & 1 & c \end{vmatrix}\) is

If n be any integer, then \(n(n+1)(2n+1)\) is:

The equation \(3\cos x + 4\sin x = 6\) has ... solution.

If \(\sec^{-1}x = \csc^{-1}y\), then \(\cos^{-1}(1/x) + \cos^{-1}(1/y)\) is equal to

If \(\cos P = 1/7\) and \(\cos Q = 13/14\), where P and Q both are acute angles. Then the value of \(P - Q\) is

If \(\tan\theta = -4/3\), then the value of \(\sin\theta\) is

The normal at the point (3, 4) on a circle cuts the circle at the point (-1, -2). Then the equation of the circle is

The equation of bisectors of the angles between the lines \(|x| = |y|\) are

The base of vertices of an isosceles triangle PQR are Q(1, 3) and R(-2, 7). The vertex P can be

If the angles between the pair of straight lines represented by the equation \(x^2 - 3xy + \lambda y^2 + 3x - 5y + 2 = 0\) is \(\tan^{-1}(1/3)\). Where \(\lambda\) is a non-negative real number, then \(\lambda\) is

The distance of the line \(2x - 3y = 4\) from the point \((1, 1)\) measured parallel to the line \(x + y = 1\) is

If $\omega$ is a cube root of unity, then $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2})$ is

The complex numbers $z$ satisfying $\left|\dfrac{i+z}{i-z}\right| = 1$ lie on

If $A + B + C = \pi$, then $\begin{vmatrix} \sin(A+B+C) & \sin B & \cos C \\ \sin B & 0 & \tan A \\ \cos(A+B) & \tan A & 0 \end{vmatrix}$ equals

The minimum value of $x\log x$ is equal to

If $f''(0) = k$, then $\displaystyle\lim_{x\to 0} \dfrac{2f(x) - 3f(2x) + f(4x)}{x^{2}}$ equals

If $\displaystyle\int_{-1}^{4} f(x)\,dx = 4$ and $\displaystyle\int_{2}^{4} [3 - f(x)]\,dx = 7$, then $\displaystyle\int_{-1}^{2} f(x)\,dx$ equals

The equation of the curve passing through the origin and satisfying $\dfrac{dy}{dx} = (x - y)^{2}$ is

If $(\sqrt{3} - i)^{50} = 2^{48}(x - iy)$, then $x^{2} + y^{2}$ equals

If the coefficients of the $r$th term and the $(r+1)$th term in the expansion of $(1+x)^{20}$ are in the ratio $1:2$, then $r$ equals

The area of a parallelogram with diagonals $\mathbf{a} = 3\mathbf{i} + \mathbf{j} - 2\mathbf{k}$ and $\mathbf{b} = \mathbf{i} - 3\mathbf{j} + 4\mathbf{k}$ is